What This Calculator Does
The Monthly Payment from APR Calculator works out the fixed monthly payment on an amortizing loan such as a car loan, personal loan, or mortgage. Enter the loan amount, the annual percentage rate (APR), and the term in months, and it returns your monthly payment along with the total amount you will pay and the total interest over the life of the loan.
How to Use It
Enter three values: the loan amount (the principal you borrow), the APR as an annual percentage (for example 6.5 for 6.5%), and the term in months (for example 60 for a five-year loan). The calculator converts the APR to a monthly rate and applies the standard amortization formula.
The Formula Explained
The monthly payment is given by $$M = P \cdot \frac{r\,(1+r)^{n}}{(1+r)^{n}-1}$$ where \(P\) is the loan amount, \(r\) is the monthly interest rate (APR \(\div\) 1200), and \(n\) is the number of monthly payments. Dividing the APR by 1200 converts a percentage annual rate into a monthly decimal rate. When the rate is 0%, the payment is simply the principal divided by the number of months.
Worked Example
Borrow $20,000 at 6.5% APR over 60 months. The monthly rate is \(r = 6.5 / 1200 = 0.00541667\). Raising \((1 + r)\) to the 60th power gives about \(1.38335\). The payment is $$20000 \times \frac{0.00541667 \times 1.38335}{1.38335 - 1} \approx \$391.32$$ per month. Total paid is about $23,479, of which roughly $3,479 is interest.
FAQ
Is APR the same as the interest rate? For this calculation we treat APR as the nominal annual rate compounded monthly. A true APR may also include fees, so your real cost can be slightly higher.
What if my term is in years? Multiply the number of years by 12 to get months before entering it.
Does this handle a 0% promotional rate? Yes. If you enter 0 for the APR, the payment is just the loan amount divided evenly across the months.
